I don't think anyone thinks it will have an immediate change in price. The November 2012 halving and then the July 2016 halving didn't cause an immediate huge spike. I remember watching for the first post-halving block. It was like watching grass grow. But anyway, it took time for the price to increase. It wasn't until spring 2013 when it started to go up a lot (5-6 months), and then it wasn't until maybe spring 2017 after the July 2016 (6-8 months) halving that things started to look up in fiat price.
I think it went something like this: People were anticipating the halving, had bought some bitcoin beforehand hoping to make a quick buck. When it didn't spike that day, week or in the next month, people started selling think it wasn't going to happen. It took months to clear out the bitcoin people had purchased prior to the halving. Once that supply was cleared out, the impact of the limited new supply became apparent and the price ended up reflecting that over time.
So I wouldn't expect a spike in the middle of May 2020. There will likely be some increased demand between now and May because people want to get in prior to the halving so the fiat price may go up but I wouldn't expect a big spike in price on May 14th (or whenever it ends up actually occurring) for the same reasons it hasn't happened in the past.
Will the next halving result in a similar price spike as the previous ones? No one knows, but if new demand for bitcoin remains the same while the new supply is cut in half yes.